the charring of the wrapper is normal.
the coin lockout magnet/coil is pretty much powered all the time, so it gets warm and the paper wrapper ages and discolors.
the buzzing is mostly due to wear/burrs on the nubs on the coil top and dimples on the armature plate the coil is controlling. Less common is the wrong spring is on the armature - it's too strong so the armature lifts off the coil top whenever the AC voltage is crossing thru zero.
you can try filing the coil top a little, and if there's dimples in the plate you can whack the thing with a hammer on an anvil to remove them (without changing the normal bends in the armature if it has them). Works sometimes. Sometimes replacing the coil works, but it's not guaranteed.
it would be great if there was a source for new armature plates since replacing the armature and the coil almost always works, but I don't know of one.
hacky solutions are to put something on the coil top or armature plate to damp the vibration (tape or whatever). If you don't care about the game accepting coins when it shouldn't you can disconnect the coil and either remove the armature or stick a piece of paper over the hole in the back of the coin mech so the armature can't poke into the mech and deflect the coin.